Split magnet systems for hybrid imaging, such as positron emission tomography-magnetic resonance imaging (PET-MRI) and Radiotherapy-MRI, require gradient coils designed with similar shapes as their corresponding main magnet. This introduces challenges in the gradient coil design of good performance and manufacturing. In this paper the effect of the gap size in shielded transverse split gradient coils and split cryostat "warm" bore over the coil efficiency, shielding efficiency, wire spacing, cryostat ohmic power loss and mechanical vibration have been simulated and studied. A "free-surface" gradient coil design method was used to design the split, actively-shielded transverse gradient coils with an axial gap. A network method was used to calculate the eddy currents induced in the split cryostat "warm" bore. The shielding efficiency and the minimum wire spacing were found to decrease when the size of the central gap is increased. The ohmic power loss and the amplitude of the radial vibrations in the split cryostat "warm" bore increases when the gap size in the gradient coil and "warm" bore is increased. It is hoped that these investigations will be useful for the development of new hybrid imaging modalities involving MRI.